Early in this century, the Austrian mathematician J. Radon demonstrated that a planar two-dimensional slice of a three-dimensional object could be reproduced from a correctly chosen set of projections in the selected plane. CT X-ray systems generate a planar set of X-ray beam projections through an object to be examined. The resultant detected X-ray data are computer processed to reconstruct a tomographic image-slice of the object.
CT systems subject the object under examination to pencil-like X-ray beams from many different directions. In a "fan beam" system, the X-rays radiate from a point-like source and data are collected at the end points of a fan at any given moment to form a "view". By contrast, in a "parallel beam" system, a "view" is made by a number of X-rays all parallel to each other. In either system, a view is one projection of the object onto the detectors, and a scan is a collection of views with a view angle that changes from one view to the next in a systematic manner.
In a fan beam scanning electron beam system such as described in U.S. Pat. No. 4,521,900 to Rand, or U.S. Pat. No. 4,352,021 to Boyd, an electron beam is produced by an electron gun and accelerated downstream along the z-axis of an evacuated chamber. Further downstream, a "beam optical" system deflects the electron beam and brings it to a focus on a suitable target, typically a large arc of tungsten material. The electron beam, on impact with the target, gives rise to a fan of X-rays.
The emitted X-rays penetrate an object (e.g., a patient) disposed along the z-axis (typically on a couch) and lying within a so-called reconstruction circle. X-ray beams passing through the object are attenuated by various amounts depending upon the nature of the traversed object (e.g. bone, tissue, metal). A group of X-ray detectors, disposed on the far side of the object, receive the attenuated beams and provide signals proportional to the strength of these beams.
Typically the output data from the detectors are processed using a filtered back-projection algorithm. Detector data representing the object scanned from many directions are arranged to produce attenuation profiles for each direction. The attenuation profiles are then back-projected and superimposed to produce a computed tomographic image of the original object. Algorithms for such reconstruction are described in the literature, e.g. in "Principles of Computerized Tomographic Imaging" by Avinash Kak and Malcolm Slaney, IEEE Press, N.Y. (1987). The reconstructed image may then be displayed on a video monitor. As noted, the geometry of EBCT scanners produces undesired artifacts that are visible in the reconstructed displayed image.
Systems similar to what is described in the above patents to Rand or Boyd are manufactured by Imatron, Inc., located in South San Francisco, Calif. These systems are termed "short scan" because the views used for reconstructing the object image cover 180.degree. plus the fan beam angle (about 30.degree.), e.g., about 210.degree., rather than a full 360.degree..
As seen in FIGS. 1A and 1B, the source of X-rays in these systems traverses a circular path 14' that is shifted longitudinally (along the z-axis) from a circle 22' upon which detectors in a detector array 22 are disposed. The source of the X-rays thus travels within a second plane, also orthogonal to the z-axis, but not necessarily coincident with the first plane on which the detectors lie. The offset between the planes, .DELTA.z, is in the order of a cm or so. Thus, while ideally reconstruction creates an image in a plane perpendicular to the z-axis using views acquired in that plane, reconstruction of images in these systems have to use views that are not perpendicular to the z-axis.
This .DELTA.z offset causes the X-ray beam to sweep out a shallow cone during the scan. Unless this "cone beam" geometry is accounted for in the reconstruction of the image, image artifacts result. In objects that vary in attenuation along the z-axis, artifacts show as streaks in reconstruction.
U.S. Pat. No. 5,406,479 to Harman (1995) discloses a method that can take the fan beam data from these systems, use "rebinning" to form the corresponding parallel beam data, and finally apply "transform domain" algorithins that can then rapidly reconstruct the image on conventional computer array processors. This is to be contrasted with customized backprojection equipment, that makes CT systems costly and upgrades of systems time consuming. Moreover, before the Harman invention, CT system manufacturers had to rely on sole-source equipment such as backprojectors.
In the method disclosed in the Harman patent, the so-called "cone geometry problem" in image reconstruction is solved using a heuristic approach. The approach seems to work well, especially for shallow cone angle EBCT scanner systems. However it is difficult to analyze the accuracy of the Harman method, and it is difficult to extend the method, for example to the use of more than two scans, or for larger cone angles. Applicant refers to and incorporates herein by reference U.S. Pat. No. 5,406,479 to Harman for additional material set forth therein.
What is needed is an "analyzable" method for understanding and solving the "cone geometry problem" in image reconstruction of EBCT systems. Preferably, when compared to existing (heuristic) methods, such a method should function more rapidly, and improve signal/noise characteristics of the final reconstructed image in situations where the existing methods have been shown to be successful. In addition, such a method should allow easy extension to hitherto difficult settings where more than two scans or larger cone angles are involved.
The present invention provides such a method.